Correct me if I'm wrong, but Barbara post-Crisis was the daughter of Gordon's biological brother. So even if they went that route, wouldn't she still be black?
Easy fix: Put Gordon in an interracial marriage. Then either Barbara is the adopted daughter of his brother in law, or she takes after her mother in the looks department.
(Note: I would not be against a black Batgirl. I'm just giving a solution to the "How to make her a red-haired white girl "problem.")